Exponents

Exponents are a shorthand way of representing repeated multiplication of the same number. The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

Basic Terminology:

Base: The number that is being multiplied in the expression. For example, in 2³, 2 is the base.
Exponent: The number that represents how many times the base is being multiplied. In the expression 2³, 3 is the exponent.
Power: The result of raising a base to an exponent. In 2³, the power is 8.

Rules of Exponents:

Product of Powers: When multiplying two powers with the same base, add the exponents. For example: 2³ * 2⁴ = 2⁷.
Quotient of Powers: When dividing two powers with the same base, subtract the exponents. For example: 2⁵ / 2² = 2³.
Power of a Power: When raising a power to another power, multiply the exponents. For example: (2³)² = 2⁶.
Zero Exponent: Any non-zero number raised to the power of 0 is 1. For example: 5⁰ = 1.
Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example: 2^-3 = 1/(2³).